Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2026-11-01 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
2nd|0th → 5
⟨⋯ 2 ⋯ 5 ⋯ 6 ⋯ 0 ⋯⟩
⟨⋯ Perm(4,5,6) ⋯⟩
⛔Avoid
⟨⋯ ᵃb ⋯⟩, |a-b|=4
⟨⋯ 3 ⋯ 2 ⋯ 0 ⋯⟩
#125034_v2.15
2026-10-30 Q1(m=6,v=0)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
max ⊢3⊣ = 4
max ⊢1⊣ = 4
min ⊢3⊣ ≤ 2
⛔Avoid
min ⊢6⊣ ≤ 2
max ⊢0⊣ ≥ 4
min ⊢2⊣ ≥ 1
1 ∾ 5
#125034_v2.15
2026-10-30 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨⋯ ? ⋯ 0 ⋯ (?−3)⟩ (?≠3)
⟨⋯ ᵃb ⋯⟩, ab=20
⟨ ▧ − − − ▢ ▢ ⟩, ▧ ≥ Σ▢
⛔Avoid
min ⊢3⊣ ≤ 2
Jump(0,5) = 1
⟨ ¹ˢᵗb ⁰ᵗʰa ⟩, a > b
#125034_v2.15
2026-10-29 Q1(m=6,v=1)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
5th|4th|3rd|0th → 1
1st → 6
5th → 3
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, max⟦a,b⟧ = 5
⛔Avoid
⟨ ⁶ᵗʰa ⁴ᵗʰb ⟩, min⟦a,b⟧ = 0
6th|4th|3rd|0th → 4
⟨ ⁶ᵗʰa ⁴ᵗʰb ⟩, min⟦a,b⟧ = 2
#125034_v2.15
2026-10-29 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟦1,2⟧ ∋ 3
⟨ − − ▧ − ▢ ▢ ⟩, ▧ ≥ Σ▢
⟨ ⁵ᵗʰb ⁴ᵗʰa ⟩, a > b
⛔Avoid
max ⊢0⊣ ≥ 3
⟨ ▧ ▧ ▢ ▢ ▢ − ⟩, Σ▧ ≤ Σ▢
#125034_v2.15
2026-10-27 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨ ³ʳᵈa ¹ˢᵗb ⟩, min⟦a,b⟧ = 2
⟨⋯ 3 ⋯ 2 ⋯⟩
2nd|0th → 0
⟨⋯ ᵃb ⋯⟩, ab=2+7n
⛔Avoid
median {p4, p2, p0} = 1
Jump(3,4) = 1
⟨⋯ 5 ⋯ ? ⋯ 2 (?−3)⟩ (?≠5)
{p4, p2, p1} = ? + {0,2,3}
#125034_v2.15
2026-10-27 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
1st → a, 0th → b, ab=1+3n
⟨? ⋯ 2 ⋯ (?+4) ⋯⟩ (?≠2)
4th → a, 1st → b, ab=2+7n
⟦3,4⟧ ∋ 1,6
⟨ ³ʳᵈa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 423
#125034_v2.15
2026-10-25 Q1(m=6,v=1)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨⋯ ᵃb ⋯⟩, ab=5
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 23
⟨ − − ▧ ▧ ▧ ▢ ▢ ⟩, Σ▧ ≥ Σ▢
⛔Avoid
⟨⋯ ᵃb ⋯⟩, a+b=8
⟨⋯ ᵃb ⋯⟩, ab=3
⟨⋯ ᵃb ⋯⟩, ab=20
⟨⋯ ᵃb ⋯⟩, a+b=7
⟨⋯ ᵃb ⋯⟩, a+b=3
⟨ ▧ − − ▢ ▢ − − ⟩, ▧ ≥ Σ▢
⟨⋯ ᵃb ⋯⟩, a+b=5
#125034_v2.15
2026-10-25 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨ − − − ▧ ▢ ▢ ⟩, ▧ ≥ Σ▢
3rd → a, 2nd → b, ab=5+10n
5th → a, 3rd → b, ab=2+10n
⟨⋯ ? ⋯ 4 ⋯ (?−2)⟩ (?≠4)
5th|3rd|1st|0th → 3
#125034_v2.15
2026-10-23 Q1(v=1)
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
Jump(3,5) = 0
⟨⋯ Perm(0,3) ⋯⟩
Jump(2,5) = 1
⟨Perm(2,4,5) Perm(0,1,3)⟩
#125034_v2.15
2026-10-23 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨⋯ Perm(1,2,4) ⋯⟩
4th → a, 0th → b, a+b=3+5n
⛔Avoid
⟨⋯ 5 ⋯ 2 ⋯ 3 ⋯⟩
⟨⋯ ᵃb ⋯⟩, |a-b|=0
Jump(0,1) ≥ 2
#125034_v2.15
2026-10-22 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
{p4, p2, p1, p0} = ? + {0,1,3,4}
⟨⋯ 6 ⋯ 1 ⋯⟩
⟨⋯ ? ⋯ 5 ⋯ (?+4)⟩ (?≠1)
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 6
⛔Avoid
⟨ − − − ▧ ▧ ▢ ▢ ⟩, Σ▧ ≥ Σ▢
6th → a, 1st → b, ab=5+10n
#125034_v2.15
2026-10-22 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
{p4, p2, p0} = ? + {0,1,2}
⟨⋯ ᵃb ⋯⟩, |a-b|=4
{p5, p4, p3} = ? + {0,1,2}
⛔Avoid
⟨ ¹ˢᵗ↓ ⟩ after 3×⟨→⟩
⟨⋯ ᵃb ⋯⟩, ab=10
#125034_v2.15
2026-10-20 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
Jump(0,4) = 2
⟨⋯ Perm(2,3) ⋯⟩
⟨ ⁴ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 420
2nd → a, 0th → b, a+b=7
⛔Avoid
⟨⋯ ᵃb ⋯⟩, ab=6+7n
#125034_v2.15
2026-10-20 Q1(m=6,v=0)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
{p6, p4, p2} = ? + {0,1,2}
{p4, p3, p1, p0} = ? + {0,1,2,3}
{p6, p3, p0} = ? + {0,2,4}
⟦0,1⟧ ∋ 2,3,4
#125034_v2.15
2026-10-18 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨⋯ 2 ⋯ 4 ⋯ 1 ⋯ 6 ⋯⟩
⟦0,6⟧ ∋ 2,3,4
{p6, p5, p3} = ? + {0,1,2}
⟨ ³ʳᵈa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 150
⛔Avoid
5th → a, 1st → b, ab=10+7n
#125034_v2.15
2026-10-18 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, (ab)₁₀ ≤ 23
⟨⋯ 2 ⋯ 1 ⋯ 5 ⋯⟩
⟨ ³ʳᵈc ²ⁿᵈa ⁰ᵗʰb ⟩, a > b > c
⛔Avoid
max {p4, p2, p0} = 5
#125034_v2.15
2026-10-16 Q1(v=1)
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
max ⊢2⊣ = 3
5th → a, 0th → b, ab=10
3rd → a, 1st → b, ab=4
5th → a, 1st → b, ab=2
#125034_v2.15
2026-10-16 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨ ⁵ᵗʰb ⁴ᵗʰa ⟩, a > b
⟨⋯ ? ⋯ 3 ⋯ (?−2)⟩ (?≠3,5)
⟨⋯ 0 ⋯ ? 3 ⋯ (?−3)⟩ (?≠3)
⟨⋯ ᵃb ⋯⟩, ab=5+3n
#125034_v2.15
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